{"id":219,"date":"2018-12-29T15:38:52","date_gmt":"2018-12-29T20:38:52","guid":{"rendered":"http:\/\/josmfs.net\/wordpress\/?p=219"},"modified":"2025-07-28T19:14:12","modified_gmt":"2025-07-28T23:14:12","slug":"keplers-laws-and-newtons-laws","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2018\/12\/29\/keplers-laws-and-newtons-laws\/","title":{"rendered":"Kepler\u2019s Laws and Newton\u2019s Laws"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-216\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2018\/12\/Keplers-and-Newtons-Laws-Ellipse.jpg\" alt=\"\" height=\"89\" width=\"200\">Years ago (1963) I got the paperback <em>The Calculus:A Genetic Approach<\/em>, by Otto Toeplitz, which presented the basic ideas of the differential and integral calculus from a historical point of view. One thing Toeplitz did at the end of his book that I had not seen in other texts was to show the equivalence of Kepler\u2019s Laws and Newton\u2019s Law of Gravity. (Since 1963 David Bressoud has developed this theme in his excellent 1991 text.) I thought I would try to emulate Toeplitz&#8217;s approach with more modern notation (vectors) and arguments in hopes of extracting the essential ideas from the clutter.<\/p>\n<p>A by-product of this effort was to reveal strongly the different paths that physics and mathematics follow in understanding physical reality.&nbsp; The mystery is that the mathematics ends up describing the physics so well.&nbsp; I will return to this theme a number of times in other posts.&nbsp; See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2018\/12\/Keplers-and-Newtons-Laws-180521.pdf\">Kepler&#8217;s Laws and Newton&#8217;s Laws<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Years ago (1963) I got the paperback The Calculus:A Genetic Approach, by Otto Toeplitz, which presented the basic ideas of the differential and integral calculus from a historical point of view. One thing Toeplitz did at the end of his book that I had not seen in other texts was to show the equivalence of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[40,32,286,19,10,11,7,39,14,31],"class_list":["post-219","post","type-post","status-publish","format-standard","hentry","category-math-inquiries","tag-analytic-geometry","tag-calculus","tag-david-bressoud","tag-equal-areas-law","tag-newton","tag-kepler","tag-math-history","tag-otto-toeplitz","tag-physics","tag-vectors"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/219","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=219"}],"version-history":[{"count":6,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/219\/revisions"}],"predecessor-version":[{"id":283,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/219\/revisions\/283"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=219"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=219"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=219"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}